Nash Equilibrium Optimization Control Method for Formation Problem of Non-Cooperative Swarm Systems

doi:10.3778/j.issn.1002-8331.2309-0140

Abstract

Abstract: A distributed non-cooperative optimization control method is proposed for the formation control problem for swarm systems. Firstly, a mathematical model of the formation control for swarm systems and individual cost function are established, and a distributed control protocol framework is designed using consensus strategy. Secondly, the framework for the control protocol with parameters is designed based on Nash equilibrium theory. Then, necessary and sufficient conditions for the time-varying formation of the swarm systems are given, and the stability of the system and parameter selection methods are analyzed using the Lyapunov method. Finally, the effectiveness of the method is verified through the simulation experiment and the improvements in optimization performance and convergence speed.

Key words: non-cooperative optimization, swarm systems formation control, Nash equilibrium, distributed

摘要： 针对群系统编队控制问题，提出了一种分布式非合作优化控制方法。建立了群系统编队控制问题的数学模型和个体代价函数，采用一致性策略设计了分布式控制协议框架。基于纳什均衡理论设计了带参控制协议框架。给出了群系统形成时变编队的充要条件，并利用李雅普诺夫方法分析了系统的稳定性和参数选取方法。仿真实验验证了方法的有效性，以及在优化性能和收敛速度方面的改进效果。

关键词: 非合作优化, 群系统编队控制, 纳什均衡, 分布式

CHEN Hongwei, ZHANG Qingjie, GE Yuanzheng, ZHOU Wenhong. Nash Equilibrium Optimization Control Method for Formation Problem of Non-Cooperative Swarm Systems[J]. Computer Engineering and Applications, 2024, 60(7): 84-91.

陈宏伟, 张庆杰, 葛渊峥, 周文宏. 非合作群系统编队问题的纳什均衡优化控制方法[J]. 计算机工程与应用, 2024, 60(7): 84-91.

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